A graph-theoretic framework for algorithmic design of experiments

TL;DR

This paper introduces a graph-theoretic approach that leverages automorphisms to efficiently identify optimal experimental designs, especially in network-structured and block design experiments, reducing computational effort.

Contribution

It presents a novel framework that exploits graph automorphisms to accelerate the search for optimal experimental designs, including those without inherent network structures.

Findings

Automorphisms significantly reduce evaluation counts for network-structured designs.

Adding block nodes induces network structures in traditional block designs, enabling automorphism use.

The approach accelerates optimal design identification across various experimental types.

Abstract

In this paper, we demonstrate that considering experiments in a graph-theoretic manner allows us to exploit automorphisms of the graph to reduce the number of evaluations of candidate designs for those experiments, and thus find optimal designs faster. We show that the use of automorphisms for reducing the number of evaluations required of an optimality criterion function is effective on designs where experimental units have a network structure. Moreover, we show that we can take block designs with no apparent network structure, such as one-way blocked experiments, row-column experiments, and crossover designs, and add block nodes to induce a network structure. Considering automorphisms can thus reduce the amount of time it takes to find optimal designs for a wide class of experiments.